431 
Mr. Ivory on the astronomical refractions. 
the temperature and pressure of the lowest stratum of air 
and upon the radius of the earth, the formula involves no 
hypothesis concerning the gradation of heat or density. But 
if the expansion of the expression of the refraction be ex- 
tended to more terms, we meet with quantities that cannot 
be integrated without supposing a relation between s and u, 
that is, without introducing a supposition respecting the con- 
stitution of the atmosphere. 
The ultimate deviation of the light of a star from its 
primitive direction depends upon the augmentation of the 
velocity which the light acquires in its passage through the 
atmosphere, and likewise upon the different obliquities with 
which it crosses the several strata of air. Now, the first of 
these two things is the same for all stars and for all constitu- 
tions of the atmosphere ; for it is the same when the density 
of the lowest stratum of air continues the same. But the 
second is different for stars that are differently placed with 
regard to the zenith : and it varies also with the densities of 
the strata that compose the atmosphere. It is therefore cer- 
tain that the formula of Laplace is rigorously exact in no 
case whatever. But when a star is near the zenith, the varia- 
tions in the obliquity of the light in passing through the 
several strata of air, are inconsiderable ; and the formula will 
be nearly true. However, there is always some error, which 
accumulates as the zenith distance increases, and will at 
length become sensible. Delambre tells us that in comparing 
the observations of different days, he found errors arising 
from refraction that amounted to 6 " or 7" at 75 0 from the 
zenith ;* and the observations of a very accurate astronomer 
* Astron. Vol. i. p. 320. 
